Surface Wave Scattering and Mode Coupling: Implications for Surface Wave Tomography

The importance of surface wave mode coupling when modelling body-wave phases by surface-wave mode summation is now well understood but many surface-wave tomography techniques continue to rely on the assumption of modes propagating independently from source to receiver. We present an investigation into the pitfalls of this assumption at periods shorter than about 50s. Synthetic tests are conducted using a finite difference solution of the elastic wave equation in 2D Earth models that consist of a region of lateral heterogeneity imposed on a laterally homogeneous background medium. Green's functions in the background medium are computed numerically and the finite difference algorithm is used only to compute the scattered wavefield produced by the heterogeneity, so this approach allows us to see how a single mode incident on the heterogenous region emerges from it as a multimode wavetrain. A combination of dispersion analysis and eigenfunction decomposition of the emergent wavefield is used to study the exact redistribution of energy among the surface-wave modes. This is then checked against theoretical multiple scattering methods which exploit the concept of invariant embedding and are able to exactly describe surface-wave mode coupling. The synthetic seismograms generated in our tests as described above are inverted using a multimode inversion technique which decomposes a waveform into a set of independent modes. We find strong artefacts in the path average models obtained by such an inversion. It is demonstrated that whilst the inversion is successful in cases where the measured modes are generated at the source, it fails in cases where any of the measured modes are generated by mode conversions along the horizontal path from source to receiver. Since inversion for path average medium properties is often the first part of two-step tomographic procedures, our results have strong implications for surface-wave tomography.